THIS IS A RUSH TRANSCRIPT. THIS COPY MAY NOT BE IN ITS FINAL FORM AND MAY BE UPDATED.

WOLF BLITZER, HOST: It's noon in Washington, 9 a.m. in Los Angeles, 7 p.m. in Ramallah on the West Bank, and 8 p.m. in Baghdad. Wherever you're watching from around the world, thanks very much for joining us for "LATE EDITION". In this hour, our exclusive Sunday interview with the wife of the vice president, Dick Cheney. We'll ask Lynne Cheney about the vice president's sudden trip to the hospital yesterday and how he's doing today.

And in a few moments, two leading members of the U.S. Senate weigh in on the latest effort to crush the insurgency in Iraq and what it all means for that country's planned elections at the end of January.

We'll get to all of that. First, though, let's get a quick check of what's making news right now.

(NEWSBREAK)

BLITZER: There's been a major development in the aftermath of Yasser Arafat's death. Masked men have just opened fire today near a mourning tent in Gaza shortly before a visit by the former Palestinian Prime Minister Mahmoud Abbas, someone slated to perhaps become the new Palestinian leader.

Meanwhile, Palestinian officials are making a number of changes to try to establish their new leadership.

CNN's Matthew Chance is just back from Ramallah. He's joining us live in Jerusalem with details.

First of all, Matthew, was this an assassination attempt by Palestinians against Mahmoud Abbas?

MATTHEW CHANCE, CNN CORRESPONDENT: Wolf, it doesn't seem that it was, at least that's according to Mohamed Dahlan, who's a senior figure of the Fatah movement in the Gaza Strip. He said this was not an assassination attempt against Mahmoud Abbas, also known as Abu Mazen.

It seems that what happens is the group of 12 gunmen burst into the tent into which mourners gathered to mourn the death of Yasser Arafat and fired shots into the air. The bodyguard of Abu Mazen, the former Palestinian prime minister, also fired their guns into the air. And in this sort of confrontation that followed that lasted, according to eyewitnesses around five minutes, we're now hearing from hospital sources in Gaza that at least two people were killed, both of them Palestinian security officials.

There's been a lot of talk and concern, of course, over the past few days following the death of Yasser Arafat about the possibility of the sort of situation descending into a very violent, a very chaotic struggle for power.

I think this is an early example of just how dangerous the situation is for Palestinian politicians at the moment, Wolf.

BLITZER: And they've set the stage for elections, Palestinian elections, Matthew, what, January 9th throughout the Palestinian territories for these new elections. Give us a little time frame, how that's supposed to take place.

CHANCE: Well, its going to be difficult. January 9th, you're right, is the date that's been set by the Palestinian Authority to have these elections for the president of the Palestinian Authority to replace Yasser Arafat, to find a successor for Yasser Arafat, to be held.

It's going to be very difficult logistically because all the voters have to be registered. It's going to be difficult for candidates when they're declared.

And they've said they're going to declare the candidates over the next week or so to take part in this election.

But it's going to be difficult because of the Israeli presence in the West Bank, in places in the Gaza Strip, as well, for voters to be registered, for people to go from town to town to vote, for candidates to campaign.

And so Palestinian officials are appealing to the Israelis and appealing to the U.S., as well, to put pressure on the Israelis to take whatever action they can to reduce their sort of troop presence in those occupied territories to allow this election to go off as best it possibly can.

But there is this other sort of shadow of violence, as we've seen tonight, looming over the whole process, Wolf.

BLITZER: And we'll check back with you, Matthew, when we get more information on precisely what happened in Gaza literally only a few minutes ago.

Also later on "LATE EDITION," we'll speak with Saeb Erakat, the chief Palestinian negotiator, and the Israeli vice prime minister, Ehud Olmert. Much more coming up on this story.

Let's move on now to the battle of Fallujah. U.S. military officials are calling the campaign a success. Our senior international correspondent, Nic Robertson, has been embedded with the U.S. Marines. He's joining us now live from near Fallujah with all the latest developments.

Nic, what is happening today? What is this, day seven of this military offensive?

The reason U.S. officials are calling this a success, the offensive in Fallujah went more quickly than anticipated. The casualties have been lower. The intensity and the duration of some of the firefights, perhaps, less than was anticipated. Indeed, fighting to achieve those objectives has been easier than the commanders thought might happen.

What is happening now: The city has been gone through by coalition and Iraqi troops, by U.S. Marines, infantry from the 1st Infantry Division. And now they're going back through their different sectors, sweeping through those sectors looking for areas of insurgents, identifying those areas, and then taking on those insurgents, capturing them or killing them.

The city is still far from safe at this time. It is not safe enough yet for Iraqis to return. It is not safe enough yet for humanitarian missions to begin going into the city.

The situation there is that the troops that are still on the ground occasionally come across pockets of resistance. Those pockets of resistance can put up quite a fierce firefight. And the troops that are on the ground there are still in some danger when they're encountered, when they're taken on.

The problem one Marine commander told me, Wolf, was that they don't know where the insurgents are, and that is what makes them vulnerable. When they identify those locations -- sometimes that only happens after they've been shot at -- when they identify those locations, they can bring coordinated firepower to bear and then deal with those groups, Wolf.

BLITZER: Nic Robertson is embedded with the U.S. Marines in Fallujah.

Thank you, Nic, very much. We'll get back to you.

President Bush says despite the success of U.S. and Iraqi forces, the insurgent violence could very well escalate as Iraq tries to move toward its scheduled elections at the end of January.

Joining us now to talk a little bit about more and other subjects, two guests: the chairman of the Senate Foreign Relations Committee, Republican Richard Lugar of Indiana, and in New York, the top Democrat on the Senate Armed Services Committee, Carl Levin of Michigan. He's also on the Select Intelligence Committee in the Senate. Senators, thanks very much for joining us.

And I'll begin with you, Senator Lugar. The battle for Fallujah, sounds like it's basically over right now, but based on what you know, the war against the insurgency in Iraq, I take it, is far from over.

SEN. RICHARD LUGAR (R), INDIANA: Well, that's true in Fallujah. The question will be, can Iraqis then come in and patrol Fallujah, establish control? Can Iraqis do the same as Samarra, where already they seem to have been doing better, and then move on to Mosul, where we know that insurgents are now occupying a part of the city?

Our estimates are, U.S. estimates, that 115,000 Iraqis now are under arms, could be helpful as a militia or police. They claim 200,000 will be in that status by the end of 2005. But they're lightly trained.

In many cases, the situation of arms for them is suspect.

So the issue, clearly, is, can you get enough Iraqis trained to be able to govern cities so that an election can be held by Iraqis that is seen as legitimate by Iraqis, in which they all participate?

BLITZER: Because if the U.S. forces pull out of Fallujah now and the Iraqis are not yet ready to occupy and bring stability and security there, the insurgents are simply going to come back, within days presumably.

LUGAR: Well, some could. And right now, as you just reported, insurgents apparently are still in some buildings there in a mop-up operation. Iraqis are out of the place. Iraqi forces, we don't know where they are, at least how far they're coming along to pick up after the Americans. But it looks like either the Americans or the Iraqis will have to move on to Mosul or to other places, and the same situation will be there.

BLITZER: In this week-long battle, Senator Levin, it looks like the U.S. suffered some significant casualties. More than 20 dead, but hundreds of U.S. troops have been injured, have been wounded. Many of them already have been brought to Ramstein Landstuhl military base to begin the process of healing.

Is this what you, as a member of the Armed Services Committee, anticipated in this battle?

SEN. CARL LEVIN (D), MICHIGAN: Well, perhaps in this battle, we didn't have any specific numbers that we were given as to likely casualties, but this is surely not what was predicted or projected when we moved into Iraq. This is a very, very different scenario.

Forces have now been unleashed in Iraq which are going to be very difficult to control and to move into a political approach.

We've taken one step in Fallujah, but there are two key steps ahead of us, and the first step doesn't guarantee the success of either step two or three. Step two is, as you just put it, Wolf, the continued pacification of Fallujah, and as Dick just said, that's going to require Iraqis to take over, at some point fairly soon. We cannot just continue there as the target. We play right into the hands of insurgents when we do that. So step two is to transfer the security and the continued pacification of Fallujah and other places to Iraqis.

And the third step, which is very difficult, unplanned for, is the political step, which is to try to involve the Sunnis in these elections. Because otherwise we could have continued chaos and a lack of legitimacy.

So there's a long, long road ahead of us. As brilliantly as our military has fought, we have not shown an equal adeptness on the civilian side of this administration, in terms of planning for the aftermath, either the attack against Iraq or yet in Fallujah.

BLITZER: Do you have confidence, Senator Levin, in Iyad Allawi, the prime minister of Iraq, the acting prime minister, interim prime minister, that he will be able to set the stage for elections throughout all of Iraq at the end of January?

LEVIN: I think it is a very, very difficult thing to predict. Unless the Sunni community gets involved in pacifying their own areas, unless they decide that they are better off with elections than without elections, I think they're going to continue to feed this insurgency, to acquiesce in it, and that's going to make it very difficult to hold elections.

But that decision will be made by the independent election commission which exists in Iraq.

BLITZER: The secretary-general of the U.N., Senator Lugar, wrote a letter saying that he was concerned about this U.S.-led assault on insurgents in Fallujah.

Among other things he wrote, "The threat or actual use of force not only risks deepening the sense of alienation of certain communities but would also reinforce perceptions among the Iraqi population of the continued military occupation."

What do you say to the concerns raised by the secretary-general?

LUGAR: Well, they were met by United States forces, who were very, very careful to avoid civilian casualties, do any more destruction than necessary. They understand the hearts-and-minds problem the secretary is talking about.

But nevertheless, it was impossible for democracy to proceed, elections, any consideration of that, with Fallujah occupied by several thousand insurgents, some of them perhaps Sunni Iraqis, some from other countries, as they've been captured.

I think, you know, the dilemma here is that Iraqis want an election. Prime Minister Allawi has shared with a group of senators at lunch when he was here that the legitimacy of the Iraqi situation depends upon elections. So he's going to have the elections in January.

Now, he also admitted that, in some of the polling places, there could be violence. And, indeed, that's the other down side of this thing.

BLITZER: Does the United States right now, Senator Lugar, have enough troops on the ground in Iraq to prepare, to get the stage set for elections?

LUGAR: That's debatable. But we have what we have there. Probably we have enough to defeat insurgents at every single spot.

The question is, are there enough Iraqis trained at this stage to occupy those places and to provide security?

BLITZER: Here's what the president, Senator Levin, said this week about the whole issue of adequate troop levels for Iraq. Listen to what he said.

(BEGIN VIDEO CLIP)

GEORGE W. BUSH, PRESIDENT OF THE UNITED STATES: The commanders on the ground will have that which they need. And they have yet to say, "We need a substantial number of troops."

And if the commanders were to bring forth a request, I would look at it, I would listen to it very seriously and implement the request.

(END VIDEO CLIP)

BLITZER: What do you think, Senator Levin?

LEVIN: Well, two things.

First of all, the former chief of staff of the Army, when he said that they would need several hundred thousand troops there, was immediately criticized, castigated by this administration, when General Shinseki said that.

But secondly, you're not going to really get commanders asking for troops if they don't feel that their commanders want them to ask, and that's always a very, very tricky issue.

The underlying political question, which you were discussing, is whether or not the Iraqi people, particularly the Sunnis, want elections as much as we do. And they've got to want elections. They've got to be either cajoled or pushed into wanting elections as the better alternative to the status quo, or not participating in elections.

And that is where I don't see a plan or a strategy yet on the part of this administration, particularly given the Sunni clergy and the Sunni political party pulling out of that government in Iraq.

BLITZER: We're going to take a quick break, but, Senator Lugar, you want to respond quickly to Senator Levin? LUGAR: I think he makes a good point. And diplomacy now is of the essence to get the Sunnis involved and to make sure the Kurds are aboard, because that's another factor.

BLITZER: But the Kurds have always been the closest of the Iraqis to the United States.

LUGAR: That's right, but they have an agenda that Prime Minister Barzani has pointed out, of wanting a certain amount of autonomy, maybe for themselves and all of the Iraqis.

BLITZER: All right. We'll pick up that, then we'll move on. But we're going to take a quick break.

When we come back, we'll ask Senators Lugar and Levin about the Israeli-Palestinian conflict, now that Yasser Arafat has gone. Is there a new opportunity for peace?

We're also watching what's happening in Gaza right now.

Then, my exclusive Sunday interview with the vice president's wife. Lynne Cheney will join us. We'll get a first-hand account of the vice president's trip to the hospital yesterday and how he's doing today.

Later, the man in the middle of advancing the Palestinian cause, the chief Palestinian negotiator, Saeb Erekat, he'll join us. We'll talk about life on the West Bank and Gaza, after Yasser Arafat. And the peace process, can it be revived?

"LATE EDITION" continues right after this.

(COMMERCIAL BREAK)

BLITZER: "LATE EDITION"'s Web question of the week: Will Iraqi insurgents be defeated before Iraq's January elections?

You can vote. Go to cnn.com/lateedition. We'll have the results later in our program.

Senator Levin, how much of an opportunity do you believe realistically -- and you're a pragmatic, realistic guy with lots of experience in understanding what's happening between the Israelis and the Palestinians -- how much of an opportunity is there right now in the aftermath of Arafat's death?

LEVIN: I think it's a real opportunity, but whether or not it pans out will depend upon whether elections can be held -- and it looks like they will be -- before January 9th, but also what the results of that election is.

If the moderates, the people that have said before that they want to negotiate a peace agreement with Israel, that they believe in Israel's right to exist and, most importantly, those who have refused to support acts of terror and have condemned acts of terror against Israel, if they prevail and they do well in that election, then it seems to me there is a real good opportunity for peace.

But if the folks who have either justified acts of terror against civilians or who have participated and perpetrated those acts do well in the elections, then it seems to me there would be no advance at all. In fact, it could be even worse than it was with Arafat here, although that's perhaps hard to imagine at this time.

BLITZER: Listen, Senator Lugar, to what the president said Friday, President Bush, at his news conference with Tony Blair about a Palestinian state. Listen to this.

(BEGIN VIDEO CLIP)

BUSH: I think it is fair to say that I believe we have got a great chance to establish a Palestinian state. And I intend to use the next four years to spend the capital of the United States on such a state.

(END VIDEO CLIP)

BLITZER: What do you believe -- we know what the Palestinians have to do. They have to stop the terrorism, according to the president, according to Senator Levin. What do the Israelis have to do, do you believe, to help get these Palestinian elections in place by January 9th?

LUGAR: They'll have the support the idea of moderate candidates winning. Now, they're beginning to loosen up in terms of some assistance, some money that's gotten to the Palestinians; likewise, greater access of Palestinians.

But, at the same time, the tough question will be, well, if someone like Mr. Barghouti, who is in jail...

BLITZER: Marwan Barghouti.

LUGAR: ... having killed five people, but perhaps the most popular of the Palestinians in polls. And he wants to run for president.

Now, Abbas, Abu Mazen, probably is the probable moderate candidate, but the difference between the elderly Palestinians and the young people in the streets is palpable. And the question is, can you bring this together? The Israelis are a key factor. If they would say, well, we're not going to release Barghouti from jail. As a matter of fact, we're not going to have equal access to Jerusalem, a number of things.

But here maybe some of the president's capital will need to be expended, because we will probably have to move both the Israelis and the Palestinians into an election situation that is likely to be successful.

BLITZER: So do you think the Israelis should release Marwan Barghouti from jail and allow him to run for president of the Palestinian people?

LUGAR: No, I'm not suggesting they overthrow all of their laws -- although Barghouti would say he doesn't recognize any of them. We're sort of back to that question, of recognition of Israel and the status.

But the question is perhaps Barghouti can support Abbas from jail. Perhaps there is some possibility of Abbas listening to the young people, to having some counter way to, at least coming into this, that allows him to govern successfully.

BLITZER: What do you think of that, Senator Levin? Should the Israelis think of some sort a prisoner exchange, including Marwan Barghouti, who's very popular on the streets with the Palestinian rank-and-file -- he has been convicted and he's serving five consecutive life sentences, supposedly for murder and for terrorism.

LEVIN: I can understand their reluctance to allow him to leave prison, but in terms of an exchange, you're getting into an area there where I would not be in a good position to advise the Israelis.

What they are already doing, however, is releasing funds, as Senator Lugar has said, to the Palestinians, which have been held up because of Arafat's approach to the whole situation.

And also the positioning of the Israeli defense forces in Palestinian areas is going to be a critical issue for the Palestinians, as well as the Israelis, because the Israelis obviously need the security that those forces can provide, but the Palestinians do not want their presence during an election.

So how that is worked out will be very important. And the Israelis can make a major contribution if they can figure out a way to pull back some of the presence of those forces.

BLITZER: Senator Levin, I want to switch gears with you. You're a member of the Intelligence Committee. It looks like there's turmoil at the top levels of the CIA now. The new CIA director, Porter Goss, a whole bunch of career operatives and analysts are threatening to resign, if they haven't yet.

What's going on, based on what you can tell, over at the CIA?

LEVIN: Well, I think that Porter Goss apparently carried out a few things in a heavy-handed way or a precipitous way. And if that's the fact, then that would have been part of the cause here.

What I'm hoping, however, is that what's not involved is whether or not Porter Goss wants to have a stronger hand in terms of the intelligence analysis which is provided to the administration than the CIA professionals want to give to the head.

Because hopefully these CIA professionals recognize the importance of independent, objective intelligence. We saw the huge failures of intelligence before Iraq. We cannot have a repeat of that. We need more objectivity and independence.

And if that's the issue here, then it seems to me we've got to be very cautious before we just simply say we want a stronger head of the CIA, because we surely don't want a stronger political operative in the CIA.

BLITZER: One final question to you, Senator Lugar: Your Republican colleague from Pennsylvania, Arlen Specter, will you support his becoming chairman of the Senate Judiciary Committee?

LUGAR: Well, I'm going to support Republican rules, and they are that the members of the Judiciary Committee on the Republican side will nominate who that chairman ought to be.

Our rules also say that that ought to be the senior person on the committee, you know. And furthermore, term limits have limited Orrin Hatch, who has served six years. And therefore Specter is in line.

Now, those three rules are there. If Republicans decide they want to change all of them, that's a different situation. But they haven't, and therefore Specter ought to be the chairman.

BLITZER: OK. Senator Lugar, thanks very much for joining us.

Senator Levin, thanks to you as well.

Up next we'll get a quick check of what's making news right now, including today's insurgent attack in the Iraqi city of Mosul.

Then, the wife of the vice president, Lynne Cheney, she's here. We'll talk about the health of her husband, the challenge of four more years in office and her new book on George Washington.

"LATE EDITION" will be right back.

(COMMERCIAL BREAK)

(BEGIN VIDEO CLIP)

RICHARD CHENEY, VICE PRESIDENT OF THE UNITED STATES: President Bush ran forthrightly on a clear agenda for this nation's future, and the nation responded by giving him a mandate.

(END VIDEO CLIP)

BLITZER: The vice president, Dick Cheney, savoring victory the day after he and President Bush were re-elected.

Welcome back to "LATE EDITION."

There was a great deal of concern here in Washington, across the United States yesterday, when the vice president made an unexpected trip to the hospital after experiencing what was described as a shortness of breath. But after a few hours, he returned home, telling reporters he was feeling just fine.

Joining us now to talk about how the vice president is doing and more is the vice president's wife -- who knows better? -- Lynne Cheney.

Thanks very much for joining us.

LYNNE CHENEY, VICE PRESIDENT CHENEY'S WIFE: Hi, Wolf.

BLITER: You also have a new book, "When Washington Crossed the Delaware," that we're going to talk about, as well.

But everyone wants to know, how is the vice president doing?

L. CHENEY: He's fine, thank you. He's following doctor's orders. He's, you know, kind of taking the day easy, drinking -- what do you do, rest and drink plenty of liquids, when you have a cold. That's what he's doing.

BLITZER: Let me read what Dr. Reiner, Jonathan Reiner, said. He issued a statement after he was released from the hospital at G.W.

"The vice president has departed George Washington University Hospital and has returned to his residence. The vice president, complaining of a productive cough and shortness of breath, was evaluated at George Washington Medical Center today. Tests ruled out any cardiac cause of the vice president's symptoms. Tests also ruled out pneumonia and other pulmonary causes. The vice president likely has a viral upper-respiratory infection."

All right. What does that mean in English?

L. CHENEY: Well, I don't know. I mean, I guess it's a bad cold. We all had this kind of thing when we were on the campaign plane. You've been around campaigns enough to know that, you know, you see lots of people. Lots of people get sick on the campaign plane. You pass it around, and our whole family had a pretty bad cough, you know, cold kind of thing. Dick didn't get it until after the campaign was over.

BLITZER: He went hunting.

L. CHENEY: He did.

BLITZER: And he was out in Wyoming. Is that where he went hunting?

L. CHENEY: He likes to hunt for pheasant in South Dakota. BLITZER: In South Dakota.

L. CHENEY: But so anyway, he wasn't feeling well. He called the doctor, and out of an abundance of caution, they decided to, you know, run tests and be sure it wasn't cardiac-related and or something else serious, and it wasn't.

BLITZER: Well, you're his wife. You watch his health. You watch his diet. You make sure he exercises.

What exactly was he complaining of -- shortness of breath? Was it something that alarmed you personally, obviously?

L. CHENEY: No, I mean, he just told me about it, and then, you know, he made an appointment, and we went to the hospital and got it all checked out.

BLITZER: And right now he's feeling a lot better?

L. CHENEY: Oh, sure, yes.

BLITZER: Does he still have a cold?

L. CHENEY: Yes. He does, indeed.

BLITZER: And so he's just going to take it easy and tomorrow, the next few days?

L. CHENEY: Go to work tomorrow.

BLITZER: He will go back to work tomorrow?

L. CHENEY: Oh, sure.

BLITZER: So he's just drinking a lot of fluids, resting, and doing...

L. CHENEY: Doing everything you're supposed to do when you have a cold.

And I hope -- but, you know, I think really this is an important lesson for everybody. When you have symptoms that are worrisome to you at all, check it out. I mean, it's always safe to do that. And especially someone -- Dick has lived with coronary artery disease for 25 years. He is very cautious, as well he should be.

BLITZER: So even if just the shortness of breath, that's enough. But did have the EKG, and all the blood work and everything showed that there was no problem, as far as the heart was concerned, the pulmonary...

L. CHENEY: That's right. Exactly.

BLITZER: Just a bad cold. Well, give him our best wishes.

L. CHENEY: I will, thank you. BLITZER: Tell him we hope he feels a lot better. A cold can be irritating, as we all know.

Some people look at this, though, and they say, you know, he campaigned pretty hard. He did a lot of events. He even made that last-minute trip to Hawaii in an effort, unsuccessful as it turned out, to capture Hawaii.

Was it too much?

L. CHENEY: But let's go to Hawaii for a minute here, because the percentage of the Republican vote increased in Hawaii more than in any other state. So it was a trip that I think was very useful for party- building.

But you're right. He did about 280 events all around the country. We enjoyed it very much. I know people like to talk about campaigning as a grim and dismal thing, but it's really quite heartening to, you know, go out and make your case to people, to find so many supportive people, to see all the parts of this great country.

And Dick not only did campaigning on his behalf and the president's behalf, he did, I think, 75, perhaps, races for congressmen and senators and gubernatorial candidates. Neither he nor the president wanted to have a lonely victory, you know, where they won but didn't bring the House and Senate along.

So it's really remarkable and, in fact, historic they have increased their tally in the House and Senate.

BLITZER: But was it too much, though, given the history...

L. CHENEY: Oh, I don't think so.

BLITZER: He didn't complain at the time?

L. CHENEY: No. Well, I mean, every once in a while we would complain about having to stay away from home one more night.

L. CHENEY: I think everyone prefers to sleep in their own beds, but...

BLITZER: Well, he's only 63 years old...

L. CHENEY: That's right.

BLITZER: ... which nowadays is a relatively young age. He'll be, what, 67 years old in...

L. CHENEY: Well, actually, I'm 63. So I think it seems quite young.

BLITZER: It's quite young. At 63, people simply assume that he's not going to try to run for president in four years.

L. CHENEY: That's true. He said he would not. BLITZER: He's not going to run?

L. CHENEY: That's right.

BLITZER: So this is the last campaign for himself?

L. CHENEY: I know, I know. And that made it a little nostalgic. We enjoyed it so much, and at the same time, both of us knew it was the last time we would do this.

BLITZER: Why is he ruling out a run for president? Why not run for president?

L. CHENEY: He has said from the beginning that his goal was to serve this president and he didn't want to have another agenda. He makes every decision in terms of this president's welfare. And I think that's a very good way for things to be.

BLITZER: Is that an iron-clad, concrete...

L. CHENEY: Yes.

BLITZER: He's not going to change his mind?

L. CHENEY: Iron-clad, concrete.

BLITZER: All right. Let's talk a little about, you know, what you expect over these next four years. You're very well plugged in politically. We all remember you from your days you worked here as a co-host of "Crossfire" on CNN.

What do you believe are the president and the vice president's top priorities for the next four years? What should they be?

L. CHENEY: Well, first will be national security, you know, continuing to work to make the homeland safe as the president has already been working to do and continuing to pursue aggressively the enemy wherever he is, the terrorists wherever they are, wherever they plot and plan; to bring success to the Iraqi people as they struggle toward democracy; to continue to help the people in Afghanistan.

I mean, it's such a remarkable story if you think about it. When we came into office, the Taliban were in control in Afghanistan. The terrorist training camps were turning out thousands upon thousands of terrorists.

Now we're about to see the inauguration of a democratically elected president. Half of the 10 million who registered to vote are women. What a remarkable success story.

And I do believe we'll see the same kind of success in Iraq. It's harder, but we will be successful.

BLITZER: What about domestically, the biggest priorities?

L. CHENEY: Well, I think homeland security will be right there. The president's talked about making Bush tax cuts permanent. I'm sure that will be at the top of his agenda.

He has talked about a bipartisan effort to reform Social Security, to make sure that it's there, not just for the people who are retired now, those who are near retirement, but for kids in their 30s -- kids in their 30s -- young people in their 30s, my daughters and their peers, because they don't have any faith that Social Security will be there. I think they've got reason for doubting. And the president has resolved that he'll fix that.

BLITZER: Under Social Security, reforming some -- privatizing at least a chunk of it, a small chunk of it. At the same time, simplifying the tax codes. That's what he's spoken about.

L. CHENEY: Simplifying the tax code, exactly right.

BLITZER: Some of his more conservative supporters, Dr. James Dobson, for example, was on ABC last week. I want you to listen to what he said, because he thinks that the president has to move on some of these so-called moral issues. Listen to what he said.

(BEGIN VIDEO CLIP)

DR. JAMES DOBSON, FOCUS ON THE FAMILY: I think that this president has two years, or more broadly the Republican Party has two years, to implement those policies, or certainly four, or I believe they'll pay a price in the next election.

(END VIDEO CLIP)

BLITZER: He was talking about issues like abortion, ending abortion rights for women, considering judges, a constitutional amendment that would ban same-sex marriage.

Does he speak, do you think, you know, for the president and the vice president that you know?

L. CHENEY: Well, I think what the president has made very clear -- and I've been impressed by the way he's proceeded on abortion, for example, to talk about the fact that it's a very divisive issue. There are people who feel strongly on both sides, but that there are areas where we can reach common agreement.

One of those is partial-birth abortion. And that was a clear distinction between the Republican ticket and the Democratic ticket this time. The president signed a ban on partial-birth abortion, which President Clinton had refused to do and which I don't believe a Kerry administration would have done.

To move forward so that there's parental notification for abortion; to Lacy's Law, the idea that if you should -- an awful circumstance -- a mother should be murdered carrying a child that the unborn fetus is a victim as well.

So the president has been very clear about trying to find ground where we can move forward together. He has also been very clear that when he appoints judges, he wants judges who strictly interpret the Constitution and not make up law as they go along.

And I have to tell you when we were out on the campaign trail, one issue that rang a very deep chord with people was the Pledge of Allegiance issue, you know, the decision by the 9th Circuit that Americans were not supposed to say "under God" when they pledge allegiance to the flag.

People were still angry about that. And, you know, you could really get a lot of cheers by saying, you know, "We believe that we should be able to say that."

And you would get additional cheers, Dick would, when he'd go on to say, you know, "There shouldn't even be a question about it, and there wouldn't be if we had more sensible judges on the federal bench."

BLITZER: So he's going to move on that. All right, I want to...

L. CHENEY: So this is an important issue.

BLITZER: I want to take a quick break, but we have a lot more to talk about, including your new book, "When Washington Crossed the Delaware: A Wintertime Story For Young Patriots."

L. CHENEY: Good.

BLITZER: We'll talk about that and more, right after a short break.

More "LATE EDITION" right after this.

(COMMERCIAL BREAK)

BLITZER: Welcome back to "LATE EDITION." We're continuing our conversation with Lynne Cheney, the wife of the vice president.

We'll get to the book in a second. A quick follow-up to one comment you made after the last debate between John Kerry and President Bush, I want to play it for our viewers and get your thoughts on it, on what you said now. Listen to this.

(BEGIN VIDEO CLIP)

L. CHENEY: This is not a good man. And, of course, I am speaking as a mom and a pretty indignant mom. This is not a good man. What a cheap and tawdry political trick.

(END VIDEO CLIP)

BLITZER: What about that? How do you feel about what you said now that you've won?

L. CHENEY: I feel as though Senator Kerry gave a gracious concession speech and we should move on.

BLITZER: So you're not going to look back?

L. CHENEY: To my book, for example.

BLITZER: Let's talk about your book...

L. CHENEY: Good.

BLITZER: ... "When Washington Crossed the Delaware." It's a children's book, although someone like me who loves American history, I learned from reading this book.

Let me read a quote from the book because it tells a lot about George Washington.

"Washington promised extra pay to those who would serve longer, and he appealed to their love of their country. 'This was an hour of destiny,' he told one regiment, 'a time that would decide America's fate.'"

It says a lot about George Washington. What does it say about why you decided to write this book?

L. CHENEY: Well, it's a wonderful story. It's been compelling to people who love history ever since it happened. There's a great quote in the front from Abraham Lincoln. He talks about how this story has been important to him, and he's remembered it and wondered at it throughout his life.

So it's a great story. It tells about brave men changing the course of history.

BLITZER: This was really a turning point in the Revolutionary War. I mean, we all grew up believing that, but in your research, it turned out to be true.

L. CHENEY: Oh, absolutely. I mean, the British -- we had signed the Declaration of Independence six months before. The British had kicked us out of New York. They had pushed us all the way across New Jersey. The troops had crossed the Delaware River in a panic almost, got to the other side.

They had no blankets, no tents, most of them had no shoes. They were walking with rags wrapped around their feet. They had no winter clothes. It is a dire situation.

And Washington does such a bold and daring thing. He decides to attack.

BLITZER: And we're showing our viewers some of the illustrations from the book, which are beautiful illustrations.

L. CHENEY: Peter Fiore is the illustrator. Wonderful oil paintings that he did for the book. BLITZER: Another quote or two from the book: "Crucial to success was the spirit of the American troops. Beaten down as they were, could they fight another battle?"

And then you write: "General Washington and his men had stood with their country in a time of crisis. When they were cold and hungry, they did not quit. When the conflict was hard, they fought on."

How courageous...

L. CHENEY: And when they won, the glory was sweet. The victory was sweet.

BLITZER: I see you've memorized the book. Is that what you're saying?

(LAUGHTER)

L. CHENEY: That's right.

BLITZER: The lessons for today, because the U.S. is at war today...

L. CHENEY: Exactly.

BLITZER: .. there's a war on terrorism, there's a war in Afghanistan, there's a war in Iraq -- what lessons should young people reading this book learn that are applicable to today?

L. CHENEY: Well, one is, I think, about the admiration we should have for the brave men in this case -- it's now brave men and women -- who fight to defend freedom. That's certainly an important one.

Another one is that freedom isn't necessarily inevitable. I think, you know, we go about our daily lives and we enjoy the privilege of being Americans, but I think we don't understand perhaps every single day that things might have gone another way, that we might not have in the beginning become a free and independent country.

That's a pretty good realization. I think it helps make you feel more grateful about being an American, more fortunate. And that's something I think we should encourage.

BLITZER: But warfare is brutal, as we all know.

L. CHENEY: Well, and I did not hide that in the book.

BLITZER: "Saving Private Ryan," the great film by Steven Spielberg that aired on many but not all ABC stations this past week. Several ABC affiliates thought the first 20 minutes were simply too violent and depicted warfare in such a brutal but accurate way they didn't want to air it.

Did they do the right thing? L. CHENEY: Oh, I wouldn't want to second-guess their decisions, but it did surprise me that it caused such angst. It is very violent in the beginning, but it's not gratuitous violence.

And, you know, I probably wouldn't have let my grandchildren watch, but it's when I see gratuitous, senseless, pointless violence on television, or other things that, you know, children shouldn't watch that I become indignant.

BLITZER: So what are you going to do for the next four years, now that you don't have to campaign anymore?

L. CHENEY: Well, I continue to push the idea that we should do a better job of helping our kids understand the history of this great nation. Indeed, one of the ways for us to do that best is to become more knowledgeable about it ourselves.

All the proceeds from my books go to charity, so I have the privilege of, you know, finding great places around the country where people are encouraging the study of history, everything from the Rosie the Riveter Memorial in California, where they're building an institution that will help people understand the role women played in World War II, to the Frederick Douglass's House, which is close by here in Washington, to Elizabeth Cady Stanton's house in Massachusetts, to the D-Day Museum in New Orleans, which is wonderful for...

BLITZER: It's fun to give away money to good causes.

L. CHENEY: That's exactly right.

BLITZER: Lynne Cheney, give your husband, the vice president of the United States, our best wishes for a quick, quick defeat of that cold.

L. CHENEY: OK, thanks, Wolf.

BLITZER: Appreciate it very much.

L. CHENEY: Thank you.

BLITZER: And, to our viewers, please don't forget our Web question of the week: Will insurgents be defeated before Iraq's January elections?

You can vote right now. Go to cnn.com/lateedition. We'll have the results later in "LATE EDITION."

Still ahead, does the death of Yasser Arafat mean a revival of the Middle East peace process? We'll get Palestinian and Israeli perspective.

More "LATE EDITION" right after this.

(COMMERCIAL BREAK)

BLITZER: Welcome back to "LATE EDITION."

We'll get military insight into the battle for Fallujah and what U.S. and Iraqi forces can expect next, just coming up in a few minutes.

First, though, let's get a quick check of what's making news right now.

(NEWSBREAK)

BLITZER: On day seven of the battle for Fallujah, the campaign appears to be nearing what U.S. military commanders describe as a successful end for U.S. and Iraqi forces.

CNN's Jane Arraf is embedded with the U.S. Army. She's joining us live now on the telephone with all the latest developments.

Jane, what are you seeing? What can you tell us?

JANE ARRAF, CNN CORRESPONDENT: Wolf, it's relatively quiet compared to the last few evenings, but this could go on for quite some time. Now, the insurgents tend to fight in the daytime rather than night.

And what we've been seeing in this eastern sector and what we have just been told are the first foreign fighters giving themselves up. Task Force 2-2 of the 1st Infantry Division we're with say they have had a Saudi national, a Jordanian and a Palestinian surrender to them. Two of them had been wounded in a firefight.

They also have evidence of foreign fighters who have been killed when a JDAM, a bomb, was launched against a building where they saw at least 20 insurgents and then saw insurgents fleeing. They said the nationalities of the dead foreign fighters include a Syrian, an Afghan, an Egyptian and a Sudanese.

There are still pockets of insurgents out there. We were speaking with one of the Marine generals here, and he tells us that he believes, though, that they have no communications left between them and very little leadership and that, although this may not end the insurgency in all of Iraq, it sends an important signal that Fallujah is no longer in the insurgents' hands.

Wolf?

(BEGIN VIDEO CLIP)

MAJOR GENERAL RICHARD NATONSKI, U.S. MARINES: As we stated on the front side, the perception of Fallujah being a safe haven for terrorists, that perception and the reality of it will be completely wiped off before the conclusion of this operation.

(END VIDEO CLIP)

ARRAF: That was Major General Richard Natonski telling us that he believes they've basically cut off their command and control center. Still, there are insurgents out there and they are still trying to attack U.S. forces.

Wolf?

BLITZER: Do U.S. forces, Marines and soldiers, Jane, stay in Fallujah now, or do they hand over the occupation, the control of the city, in effect, to Iraqi troops and they move out?

ARRAF: Well, this is one of the problems, and it's one of the things that Major General Natonski was discussing when we were speaking with him earlier today. They have found that having people from Fallujah, security forces from Fallujah, just does not work.

And what they'll have to do what they've tried to do in other places, Samarra, for instance, which is bring in Iraqi police, bring in security forces from other centers. That's going to take a while.

And until they do that, the Marines particularly are not likely to be able to lead. The Army, which has basically brought in the armor and done the heavy lifting here, will be pulling out shortly. But they will be leaving the Marines.

Wolf?

BLITZER: Jane Arraf reporting for us in Fallujah.

Jane, thank you very much.

Let's move on elsewhere in the Middle East now. Gunfire erupting today as the former Palestinian prime minister, Mahmoud Abbas, visited a tent of mourners for Yasser Arafat in Gaza.

CNN's Matthew Chance is joining us now live from Jerusalem with details.

Matthew, we're getting additional information on precisely what happened. Can you put together, based on all the different accounts, what we know?

CHANCE: Well, details still pretty sketchy. It's coming from eyewitnesses on the ground in Gaza. There were a lot of television cameras there, as well, obviously, covering the visits of Abu Marzen, the former Palestinian prime minister and other Palestinian officials, as well, to this official mourning tent in Gaza that was set up in order for people to go and pay their respects to the former Palestinian President Yasser Arafat, who of course died on Thursday.

It seems that when Abu Marzen was inside though, about 20 gunmen burst into the tent, fired their automatic weapons over the heads of the mourners through the canvas of the tent, you know, up into the air.

Bodyguards surrounding Abu Marzen and other Palestinian officials, they also fired their weapons as well, but it seems they fired them also into the air.

What followed was a kind of very tense standoff where gunshots were fired for about five minutes. It wasn't exactly a gun battle as such. But in the chaos, it seems that at least two people according to medical officials were killed, both of them said to be members of the Palestinian security forces.

All this of course comes, Wolf, as the Palestinian Authority announces that it will hold elections to choose a successor to Yasser Arafat on January the 9th. That's, of course, early next year. And this sort of looming violence, this looming shadow of violence hanging over that process, making the selection of a new president who can unify these Palestinian factions all the more urgent, Wolf.

BLITZER: All right. Matthew Chance reporting for us from Jerusalem.

Later this hour on "LATE EDITION," we'll get some more insight, what's happening in the Middle East, the effort to try to revive the Israeli-Palestinian peace process. Saeb Erakat, the chief Palestinian negotiator, and the vice prime minister of Israel, Ehud Olmert, they'll join us. That's coming up on "LATE EDITION."

Let's move on now back to the overall situation in Iraq, the effort to stop insurgents in that country.

I'm joined now by two guests who know a great deal about what's going on: the retired U.S. Army Brigadier General James Marks. He was in charge of intelligence for coalition land forces during the invasion of Iraq last year. This is his first television interview since his retirement, which came only days ago. And in Illinois, retired U.S. Army Brigadier General David Grange. He's also a CNN military analyst, chief operation officer for the Chicago-based Mccormick Tribune Foundation.

Thanks to you both for joining us.

BLITZER: I'll begin with you, General Marks. You were a major general but you retire as a brigadier general. That's standard operating procedure, just like it was for David Grange.

BRIG. GEN. JAMES MARKS (RET.), U.S. ARMY: Well, it is, only because of the amount of time I served as a two-star.

BLITZER: As a major general?

MARKS: Right.

BLITZER: All right. So let's talk a little bit about the battle of Fallujah. You served in Iraq. You understand what's going on there right now. What is your bottom-line assessment? What is happening?

MARKS: Well, in Fallujah specifically, this is the first of many endeavors that the ground coalition forces are going to have to take on. Fallujah will set the tone.

It will also be a great opportunity not only to get our arms around insurgents, but also to gather some great intelligence that will lead us to other places, so we can really put a stop to it.

BLITZER: Well, how many places like Fallujah are there still out there?

MARKS: Well, just the other day Mosul was under some very tough fighting as well. In fact, I even think some forces were transitioned in the Fallujah area up to Mosul, to help Brigadier General Carter Ham in his endeavors up there.

BLITZER: So, Mosul, which is the second-largest city or the third-largest -- I think it's the second-largest city in Iraq-- Samarra, Ramadi, there are these pockets of insurgency all across the so-called Sunni Triangle and even beyond.

MARKS: There are. There are. In fact, you're going to see similar-type fighting that's going to take place throughout the Sunni Triangle. Again, Fallujah is the start.

BLITZER: Let me bring General Grange in.

And I want to play for you an excerpt of what Senator John McCain said earlier today on ABC, saying lots of mistakes have been made. Listen to this.

(BEGIN VIDEO CLIP)

SEN. JOHN MCCAIN (R), ARIZONA: We had to do what we did in Fallujah. We never should have given them sanctuary to start with. We made a lot of mistakes early on in this conflict.

(END VIDEO CLIP)

BLITZER: What do you think, General Grange, the mistake, the biggest mistake, not finishing the job last April, when those four American contractors were murdered and dragged through the streets?

BRIG. GEN. DAVID GRANGE (RET.), CNN MILITARY ANALYST: I believe so. In April was the time to really crush whatever insurgency was developing in Fallujah. It's always been a rat nest. And basically they had time to develop defenses, bring in more foreign fighters, to, again, as a base of operations, to raise havoc throughout other parts in Iraq.

And so, looking back, I think most of the commanders on the ground there would have liked to have gone in at that time. But it's better late than never, because it wouldn't have gotten better without an attack.

BLITZER: Well, the casualties that the U.S. facing -- more than 20 at last count. I thought 22, maybe more U.S. troops killed, but hundreds, hundreds have been injured, wounded, flown to Landstuhl near Ramstein Air Base in Germany.

It sounds like the U.S. may be paying a pretty significant price for that delay, but, correct me, General, if I'm wrong. GRANGE: Well, you know, it is a big price, but it's urban combat, and it's the toughest type. And what you have is very close face-to-face engagements. You have the ricochet and composition of city -- the cities are constructed of fragmentation that wounds a lot of soldiers.

The interesting thing is the number of deaths to wounded, and that just is kudos to the great MedEvac medical system that we have in combat for our troops. Most of the insurgents are dead. Most of the coalition are wounded.

BLITZER: General Marks, you wrote in The New York Times on Wednesday, on the op-ed page, this: "Unlike last year's invasion in which the military's primary goal was to defeat the Iraqi troops and move toward Baghdad, the fight in Fallujah is about taking terrain and holding it. It does no good to push the insurgents out and move on. They are like water; they will flow right back into any void."

Explain what you mean by that.

MARKS: Wolf, the challenge that we have in Fallujah is that we can't just simply move the insurgents out or, as Dave indicated, we're going to do a good job as the forces have done of killing those that remain.

If we don't have some transition of forces within Fallujah that can take hold of Fallujah and not give it back, it will just draw insurgents right back in.

BLITZER: Iraqi troops or U.S. troops or a combination?

MARKS: I think that what you're going to see is there will be very a deliberate transition from U.S. forces, and I would anticipate Iraqi forces at some point will complement U.S. forces. And then ideally what you're going to see is the total transition of U.S. forces out.

BLITZER: Are there enough U.S. forces, General Marks, in theater right now in Iraq to get the job done?

MARKS: The commanders on the ground would tell you that they're doing a good job with what they have. I can tell you that when we executed our ground operations last spring, in March of 2003, as decisions were made about the flow of forces into country, decisions were being made about how well we were prosecuting operations in a conventional sense against Iraqi forces as they moved to Baghdad.

So, in some cases, forces were taken off the flow to join the forces in country, but those decisions were based on success in a conventional fight. In other words, those forces would have been very handy and essential to the task of holding what we now have.

BLITZER: You say the commanders are doing a good job with what they have. That sounds to me like you think they probably need some more. MARKS: I would think that they need enough forces -- a combination of forces, Wolf. You not only need conventional forces to do the heavy lifting, as described and as we've seen in Fallujah, and that will be followed by operations elsewhere, but you also need to have, immediately on heels of those successes, you have to have what we call capabilities and forces on the ground to conduct post-combat operations, relief forces, and the ability to start the reconstruction and the rebuilding that's going to follow the destruction that occurs.

BLITZER: General Grange, that requires a lot of troops for that post-war, post-operation reconstruction or rehabilitation. Do you think the U.S. has enough troops on the ground?

GRANGE: Probably not for a counterinsurgency. And I say that because the Iraqi military, once they're trained -- and there's some units trained to standard now, some very good units, like 36th Commando -- but until they have enough boots on the ground, then the U.S. and other coalition forces are going to have to do this heavy lifting of patrolling, of occupation of urban areas after an attack in Fallujah as an example. And that takes troops. That eats up individual infantrymen.

And so, now that the momentum is set for Fallujah, why not go for it and do the same thing throughout the country and overwhelm, overwhelm with presence and contact with the civilian population and contact with the enemy, until this thing is ready for the elections in January?

And so, we may be a bit short.

BLITZER: And I want to put just briefly on the screen, before we take a break, some of the cities where fighting has erupted in Iraq since the battle for Fallujah began only last Monday, not only in Baghdad, but Balad, Baqouba, Karbala, Kirkuk, Mosul.

Significant fighting you see, General Marks. You know Iraq very well, all the way up in the north, Mosul, but a lot of those towns in the so-called Sunni Triangle, including in Baghdad.

The Sunnis, that's a big problem, to get their support for these elections scheduled at the end of January.

MARKS: Well, it really is. And what you have is a bunch of dead-enders, recidivist Baathists, that are still hanging around that didn't get the word that their leader Saddam is gone and he'll be brought to justice here shortly.

But we're going to have to continue to fight that, in every one of those locations, Baqouba, Tikrit, Baiji, elsewhere in the Sunni Triangle.

BLITZER: I'm going to ask you when we come back who these other insurgents are. Are they Iraqis? Are they foreign fighters? Who are they? What's motivating them?

But we'll take a quick break. When we return, more insight from our two generals on the Fallujah offensive. U.S. and Iraqi forces continuing to close in, as we heard from Jane Arraf, on the insurgents in Fallujah.

And later on "LATE EDITION," does the passing of Yasser Arafat open a new path to the possibility of Middle East peace? We'll talk to two top leaders from the region, Palestinian Saeb Erekat and Israeli Vice Prime Minister Ehud Olmert.

Much more "LATE EDITION" coming right up.

(COMMERCIAL BREAK)

BLITZER: Al-Jazeera reporting that the women relatives of Iyad Allawi, the interim prime minister of Iraq, who have been held hostage, held captive, by insurgents have now been released. We'll watch that story for you, get some more information on that.

We're talking about the overall battle for Fallujah, how it's unfolding, what it could mean, with two guests: retired U.S. Army Brigadier General James Marks, just retired, and retired U.S. Army Brigadier General, CNN military analyst David Grange.

We have a caller in Texas who has a question.

Go ahead, Texas.

CALLER: Yes. This is John from Texas. I want to know, will the Iraqi troops be able to maintain their own security any time soon?

BLITZER: What about that, General Marks?

MARKS: I think it's going to be a long effort. Good training is taking place right now, but there are some gaps in terms of what they bring forward, what was the foundation of their training before they decided to raise their hands and become Iraqi security forces.

So I think it's a very difficult task, but it's the one that the U.S. understands has got to be done right.

BLITZER: So, realistically, the American public should expect U.S. troops in big numbers to have to remain in Iraq for a long time to come?

MARKS: Wolf, I think so, absolutely.

BLITZER: What do you -- do you have a ballpark years, how many years?

MARKS: Oh, I mean, my guess is as good as anybody else's, but I would tell you, this is at least a four- to five-year endeavor, to make sure that we get this thing right.

BLITZER: Do you agree, General Grange?

GRANGE: I do. See, what you have to do in training, it's not just teaching people how to march and shoot. The Iraqi military had a totally different culture, an oppressive, lousy leader, lousy equipment and maintenance regimen in their military. And you have to change values before you can even attempt to change a culture, and pick good leaders, and that takes a while.

I mean, just look how long it took the U.S. Army to stay as fine- tuned as it is, and expect the Iraqis to do this overnight's just impossible. It'll take a while.

BLITZER: General Marks, I've spoken to several U.S. military personnel, civilian personnel who have worked in Iraq, who were there in the immediate aftermath of the major combat after Saddam's regime fell, in April, May, June of last year, who have recently gone back, in recent weeks, to Baghdad, to the so-called Green Zone, which supposedly is the most secure part of Baghdad.

And they all say it's day and night, that they used to be able to go out and walk around, they weren't overly concerned a year ago. Now it's almost impossible to simply roam around, even in the Green Zone, it's very, very dangerous.

Are they right?

MARKS: Wolf, there has been a year since the invasion of Baghdad and the coalition force's ability to take that city. And I need to tell you that, within the first couple of weeks that I physically was in Baghdad, there was a blanket that was over the city, there was a kind of a cathartic movement on the part of folks that were rejoicing the departure of Saddam.

So, you expected the looting, you expected to see the folks kind of taking advantage of the lack of security. But you could move, and we could move with some degrees of impunity, through Baghdad. Sadr City, it was not unusual to go to Sadr City, to put your finger on the pulse of what was really happening on a daily basis.

Over the course of the summer and up through the fall of 2003, with the porous borders that you saw, what you have is a bunch of foreign fighters, Islamic fundamentalists, jihadists that have come across the border and have really started to stir it up and take advantage of the lack of security...

BLITZER: So is it fair to say the situation, General Marks, is worse today than it was a year ago?

MARKS: I would say the security situation on the ground is worse in certain places within the cities.

But I would tell you, as a whole, what you see is in parallel, the training of the Iraqi forces, and the continuing growth and presence and training and preparedness of the U.S. forces that you're always going to see. So you've got these efforts ongoing to try to make it better.

BLITZER: General Grange, there are reports out there in the papers over the past couple of days that the insurgents are actually pretty sophisticated, learning the U.S. tactics, how the U.S. operates, even stealing uniforms, Iraqi army uniforms, and then going out and killing U.S. military personnel. If you saw a story yesterday, one Marine was killed point-blank by insurgents wearing regular Iraqi army uniforms.

How do you deal with that kind of insurgency?

GRANGE: Well, every enemy we've fought, they've learned from fighting us. I mean, it's just something that happens in the military. We do the same thing. We learn from fighting insurgents or other armies.

And the enemy are going to do anything they can, using civilians as camouflage and cover, the techniques that they use that violate the rules of land warfare, to get an advantage over a superior force.

And what you've had is, after the maneuver phase, when Saddam's regime fell, which was an excellent campaign, and then now, in fact, now, in the country with the counterinsurgency efforts, excellent work being done by our military, but the transition between maneuver combat and counterinsurgency today gave some breathing time to these internal insurgents and external foreign fighters that now put those things together and are being used against our forces and others today in Iraq, because they had too much time to breathe and get reorganized.

BLITZER: General Marks, are most of these insurgents Iraqis themselves, or what percentage of foreign fighters, people who have come in from Iran, from Syria, elsewhere in the region?

MARKS: It's a mix. What you've got is folks that have come across the border, as I said. You've got the fundamentalists and the jihadists that have come across. And...

BLITZER: What percentage of the insurgency would you guess that would be?

MARKS: Oh, I couldn't give you a good percentage that would be of value, Wolf. I couldn't do that right now.

Let me, if I can, can I make a comment about what Dave just said? You know, a military is evaluated in terms of how it executes its transitions. And that's a very subtle point that Dave just made.

And it is so very important right now that our military on the ground -- and they understand that -- go through the transition of what occurred in Fallujah, being able to take advantage of that momentum, and move that to the other locations where we have run the insurgents to, and simultaneously, being able to build that which has been destroyed to make it better so the Iraqis can take over.

BLITZER: You were in charge of intelligence going into Iraq during the invasion. Looking back -- and all of us are much smarter with hindsight, obviously -- what was the biggest mistake that the U.S. military had going into Iraq? If you could do it over again right now, what would you have fixed?

MARKS: Number one, the very largest challenge that we had is we did not understand the fear factor that existed within the normal Iraqi citizen. The regime that was in place, the fear that the average citizen had for that regime, their desires to try to rid themselves of that, and what you ended up with was forces that fought on the ground that were not necessarily, the day before, uniformed forces.

These were folks that were forced to come out, move out of the cities and to engage our formations simply because they knew that if they didn't, they would be killed, and if they went out, and if their death was the inevitable result, they had it. But at least it might have given their family an opportunity to live to see another day.

That fear factor was absolutely incredible. And I tell you what it really has to do with. You know, you've got the old expression, you keep your friends close and your enemies closer. And we didn't do that. We didn't do that in Iraq.

We didn't have sufficient presence on the ground over the course of the time from Operation Desert Storm back in the early '90s until when we executed combat operations last spring to really get a sense of what the Iraqi people were really up against.

BLITZER: General Grange, I suspect another big mistake was not sealing those borders around Iraq, Syria, Iran specifically.

GRANGE: Well, I don't think you're ever going to get 100 percent in that regard, but it's a little bit different than sealing borders of difficulty in Vietnam, maybe because of the terrain as an example.

But the borders, I think, could have been sealed much tighter. And you have to use coalition forces, because there's too many people making deals in old trade routes and stuff that go into and out of Iraq.

Wolf, one thing that's really important, I think, in this Fallujah fight -- and Jane said it earlier in the show -- now that Fallujah's taken down -- and they're going to continue to clear out pockets of resistance for quite some time. Imagine trying to find one guy here and two guys there throughout a city of this size.

The transition, the psychological effect from this fight, taking the symbol of resistance away from the insurgents, which has happened, more important than any body count, what are we going to do with that now with the momentum to use that for our effect, our advantage throughout the rest of Iraq? A very important transitional piece psychologically.

BLITZER: General Grange, thanks very much for joining us.

General Marks, thanks to you as well. Welcome to CNN. Thanks. Appreciate it very much.

MARKS: Thanks.

BLITZER: Up next, a check of what's making news right, including an update on the battle for Fallujah. Then, new hopes and challenges for the Middle East peace process in the aftermath of Yasser Arafat's death. We'll hear from both sides of the Israeli-Palestinian conflict.

Much more "LATE EDITION" straight ahead.

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BLITZER: There's been a potentially significant development involving Iran. The country, according to reports, has agreed to suspend its uranium enrichment program.

For more on this development, let's go to reporter Kasra Naji. He's joining us live by phone from Tehran.

What do we know exactly, Kasra?

KASRA NAJI, CNN CORRESPONDENT: Wolf, reports are still coming in. What we know for a fact is that Iran has decided to suspend its nuclear enrichment activities as of now.

The report basically comes from Mr. Hasan Rowhani, who is Iran's chief nuclear negotiator. And he's been talking to reporters. After a 40-minute talks with the ambassadors of three European powers -- Britain, France and Germany -- and coming out of the talks, he told reporters that Iran has decided to suspend its nuclear enrichment activities immediately. He also said that the Iran will notify the IAEA of its decision immediately.

And he says the suspension will continue as long as the talks between Iran and the European powers continue about the future of relations between Iran and Europe.

One other piece of information comes from a European diplomat who didn't want to go on the record. But he seemed very happy, saying that they, i.e. the Europeans, have got more or less, most of what they wanted from Iran.

We'll check back with you for more information as it becomes available.

Up next, charting the Palestinian future. I'll speak with the chief Palestinian negotiator, Saeb Erekat, about what's next now that Yasser Arafat is gone. Saeb Erekat joins us when we come back.

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BLITZER: The challenge for all sides in the Middle East and beyond after Yasser Arafat's death is to seize this moment if a new opportunity for peace does, in fact, exist. Just a little while ago, I spoke with the chief Palestinian negotiator, Saeb Erakat. He joined us from Ramallah on the West Bank. We spoke just before we received word of that gunfire erupting in Gaza where the former Palestinian prime minister, Mahmoud Abbas, visited a tent of mourners.

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BLITZER: Saeb Erakat, thanks so much for joining us. I know these have been very, very difficult days for you and the Palestinian people.

But you're now moving forward. I take it elections are scheduled for January 9th. Walk us through the process.

SAEB ERAKAT, CHIEF PALESTINIAN NEGOTIATOR: Today, the interim president, Mr. Rauhi Fattouh, decreed an order calling the Palestinian people of the West Bank, including Israel and Gaza, to participate in the presidential elections that will take place on the 9th of January, 2005.

On the 20th of November, it will be open for candidates and nominations from all political parties. And the system here, any Palestinian who is 35 years of age and over, irrespective of gender or political affiliation, can nominate himself. And this process will take place -- will take us 12 days till December 1st.

Then there will be a posting of the candidates, any objections. And then on December 27th, the election campaign will begin for two weeks, and the elections themselves will take place on the 9th of January.

I believe what happened so far in the Palestinian society is absolutely something to make us all proud of what we're doing in terms of the institutions, in terms of the determination by the Palestinian leadership to take our people on the path of democracy, accountability and peace. Palestinians deserve nothing less.

And I call upon President Bush to stand shoulder to shoulder with us in order to enable us to do the elections.

As far as the Israelis are concerned, I also urge them and tell them we have an interim agreement signed in 1995 concerning the elections. We carried out our elections in 1996 in accordance with this agreement. We can go with the same regulations, the same arrangements.

And the second thing they need to do is to pull their tanks and soldiers outside our populated centers in order to give the electoral process and to make it as free as possible.

I hope that the Israelis will really understand the importance of holding these Palestinian elections, because failure to do these elections will mean (UNINTELLIGIBLE) sliding further and further toward chaos, lawlessness, militias, violence and counterviolence. BLITZER: The indications you're getting from the Israelis, I take it they were fairly cooperative during the funeral process. Are you getting positive indications right now from the Sharon government?

ERAKAT: Well, it's too early to tell, actually. But you're right. We had good cooperation during the sickness of the president and the funeral processions.

And now we are in touch with the American administration, with the European Union, with the Russians, with the United Nations, in order to facilitate for us and to convince the Israeli government of the need to hold these elections.

And I urge the Israeli government also to cooperate. As I said, the 1995 agreement specified how the process of elections will take place. There are a list of not-to-do things on us, on them and a list of to-do things on us and on them. And I believe we can carry smooth, free and fair elections.

But we need to do one thing. If the Israeli tanks pull out from our populated centers, we can replace these tanks, Wolf, with American observers, British observers, French observers, whoever want to come and witness this historic moments in the making for the Palestinians.

You know, President Bush sent his troops to Afghanistan and waged a war in order to have elections there. They did the same thing in Iraq. In our case, he needs to get the army of Israel out and send civilian observers in order to see true, genuine, fair elections taking place.

BLITZER: There has been some speculation, as you know, that perhaps NATO troops should be brought in to help during some sort of transition period. Would you be open to that?

ERAKAT: Well, all we need are civilian monitors. We are willing to coordinate with the Israelis. As I said, we have an interim agreement that specified what our police will do, how the Israelis will conduct themselves on the roads and so on.

Their specifications are very well clear. It was agreed by me and my Israeli counterparts in 1995. I believe it's doable.

I believe it specifies all the security needs on our side and on the Israeli side.

And what we need to do is to cooperate with the Israelis in order to make sure that this process will be as free and fair, because, you know, it's open for anyone who run for these elections. We don't want the Israelis to stop a candidate or to arrest a candidate or to prevent someone from moving from Gaza to the West Bank, from his village to this town, because then immediately he'll be accused of rigging the elections.

So we must maintain that what we need now, we need American groups like IFUS (ph), like NDI, like the Republican Institute. We need the Europeans to send their teams immediately to the West Bank and Gaza in order to help us to carry out these elections in order to facilitate and observe and monitor that we are carrying out these elections in the total fairness that needs to be carried.

BLITZER: In the '96 elections, Yasser Arafat was elected. At that time, the Israelis allowed Palestinians living in East Jerusalem to vote. I take it that's still a sensitive issue this time, though there are indications the Israelis may relent on that.

How important is that, as far as the election process is concerned from the Palestinian perspective?

ERAKAT: It's extremely important. I don't think we can do the elections without the elements specified in the election law and the agreement signed with Israel. We don't have time to go and amend our laws now. We have less than 60 days. And I hope that the Israelis will understand.

If they study the arrangements that we did for Jerusalem, we even called the ballot stations "receptacles." And then once these five polling stations inside East Jerusalem are finished, we will take these receptacles outside Jerusalem to count outside.

I hope that the Israelis will agree with these arrangements. I hope we can go with the same specifications and the arrangements we did in 1996 because we don't have time. Time is of the essence. We should not wait for anymore.

Today, we announced the presidential decree calling for the elections on the 9th of January, because wasting any minute, Wolf -- and mark my words: This is a turning point in this region's history. If we go on the path of elections, full democracy, with American help and European help, then, trust me, this will be a turning point toward the path of democracy, peace, accountability and moderation of this region.

Failure to do so, the vacuum will be filled by more violence, more militants, more chaos, more lawlessness. And I don't know how many decades it will take us to restore back to where we are now.

So we need the Israelis to understand that time is of the essence. We need President Bush, who's been speaking about the larger Middle East and democracy. We are ready, Mr. President. Begin with us. You have a total Palestinian population that is determined to choose their leaders through a fair and free election. We don't have tribal chiefs scattered here and there. We have reached the percentage of 97 percent literacy rate.

We deserve that you stand shoulder to shoulder with us in order to enable the Palestinian people to elect their leaders freely and fairly.

And yes, we can go with the same modalities, the same arrangements we did with the Israelis in 1995. And they're doable.

BLITZER: Is Mahmoud Abbas, the former prime minister, the front- runner, would you say, right now to be the next president of the Palestinian Authority in those elections January 9th?

ERAKAT: Well, I think, you know, you can say that, but you have to wait and see. Wolf, I belong to Fatah Party. In Fatah Party, we have to do two things. The Central Committee of Fatah will have to meet, pick a candidate, and then the Revolutionary Council of Fatah will meet -- it's like a primary -- and vote and then announce officially the candidate.

This has to be done between now and the next six days, on the 20th of November. And I think we have to wait officially for the announcement of Fatah, but this process is also open to other parties. And as I said to you, any Palestinian who is 35 years of age and over can run for these elections.

BLITZER: Saeb Erekat, good luck with the elections. Thanks for spending a few moments with us. Appreciate it very much.

ERAKAT: Thank you, Wolf.

(END VIDEOTAPE)

BLITZER: And this note to our viewers: We invited the government of Israel to join us as well. The vice prime minister of Israel, Ehud Olmert, was scheduled to join us. Now we've been told he's in a high-level security briefing in Tel Aviv. We're standing by. We hope he will still join us live, perhaps on the phone. But we'll stand by to make sure we get him if, in fact, he gets to our studios on time.

Coming up, on the front lines in Iraq, a close look at what's going on on the ground in Fallujah. CNN's Nic Robertson is there.

Stay with us.

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BLITZER: Back now to the battle of Fallujah.

While the city is close to being contained, the fighting has been fierce at times. There are various threats to the troops on the ground.

CNN's senior international correspondent, Nic Robertson, is embedded with the U.S. Marines Charlie Company. He shows us a little of what they've had to face.

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ROBERTSON (voice-over): To this Marine gunner, resupplying Charley Company was never going to be easy. A high speed dash through Falluja's dangerous streets, head long into a fire fight.

A race back to base. Resupplying Charley Company no longer the objective. Better luck on the next run. Charley Company Marines rushed to get their water, food, and ammunition out of harm's way.

For their commander, the focus now on insurgent bypassed in the initial phase of the assault.

LT. COL. TRAVIS FULLER, U.S. MARINE CORPS: The threat that they pose right now is that they hold the ground. We don't know where they are. They can continue to snipe at us and fire RPGs and maybe even construct explosive devices.

ROBERTSON: Resupply Captain Tennant's Marines race for cover en route to the next objective. Plans worked out as they go.

UNIDENTIFIED MALE: If we do enough clearing rooms, if we have to take over and clear rooms, you guys are throwing a frag in every room we come to.

ROBERTSON: Explosives to clear the way. Two of Charley Company killed by insurgents lying in wait in a house just a few days before.

Past the body of a man believed to be an insurgent. Progress is cautious. Holding up in a house along the way.

UNIDENTIFIED MALE: All right, I want a scope up top. (UNINTELLIGIBLE) up there. Anderson's got us covered back here, we're good.

ROBERTSON: The strains of battle etching their wearying patterns on the face of Charley Company. No flagging though on the final push for their objective, an Iraqi school.

CAPT. THOMAS TENNANT, U.S. MARINE CORPS: One of our biggest concerns right now actually is not enemy being in the building. It's the building being booby trapped.

ROBERTSON: Later, under cover of darkness, detainees being sent back to base for questioning. And a call for much needed supplies.

As day breaks, relative quiet after a night of sporadic explosions. Time to repair, refresh, and reflect on their first taste of battle.

UNIDENTIFIED MALE: I've never gone through anything like this with one of my friends before. And I definitely know that we're all a lot closer now.

ROBERTSON: Unpredictably, and seemingly out of nowhere, they take fire. A day to be like the one before maybe. More objectives to be taken. More time for Charley Company in the firing line. Their losses so far cutting deep, but not hindering their mission.

TENNANT: Brokenhearted, disappointed, but with a mission on hand, you can't grieve too much now. You just save it and you grieve when you get out of here safely.

ROBERTSON: For Charley Company, Falluja was never going to be painless.

Nic Robertson, CNN, with Charlie Company in Fallujah, Iraq.

(END VIDEOTAPE)

BLITZER: Up next, we'll have the results of our Web question of the week. Stay with us.

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BLITZER: Here are the results of our Web question of the week. We were asking you this question: Will insurgents be defeated before Iraq's January elections?

Here's how you voted: Sixteen percent of you said yes; 84 percent of you thought no. Remember, this is not a scientific poll.

And that's your "LATE EDITION" for Sunday, November 14th. Please be sure to join me next Sunday and every Sunday at noon Eastern for the last word in Sunday talk.